how far is Xian from Chengdu?

About 800 km between them.

Thanks for the information. I am looking to come out next year. What would be the recommended mode of transportation between Chengdu and Xian?

The fastest way is taking plane.
Another way is to take the trains. If I were you, I will choose the train and buy a hard sleeper. Because the train for Chengdu will operate a night and several hours during the day time. Buying a soft sleeper, you can enjoy the beautiful scenery during the day time and have a good rest at night for the coming visiting.